WOODY Allen”s latest, and most controversial, movie is going straight to cable TV — and it”s certainly not the tepid “Small Time Crooks.”

A thoroughly outrageous religious spoof called “Picking Up the Pieces” is turning up on Cinemax beginning Friday night, apparently because the producers are having trouble lining up a theatrical run.

Nobody is confirming exactly why, but it isn”t hard to guess why distributors might have shied away from this combination of magic realism, black comedy — and barbs at organized religion that make last year”s hot potato, “Dogma,” seem reverent by comparison.

Working under the direction of Alfonso Arau (the acclaimed “Like Water For Chocolate”), Allen gets top billing as Tex, a kosher butcher from New York who”s relocated to Texas under the witness protection program.

In a jealous rage, he fantasizes he”s a magician performing a trick and takes a chain saw to his unfaithful wife Candy, played by Sharon Stone with a New York accent and a black wig.

Candy”s dismembered hand — complete with turquoise nail polish and an upraised middle finger — is discovered in the desert by a blind woman, who is miraculously cured.

She takes it to the parish priest (David Schwimmer), claiming it”s the hand of the Virgin Mary.

Distracted by his affair with the town whore, the priest puts it on display in the church — where it draws a steady stream of the faithful. Miracles are performed on an acne-pocked adolescent, a legless man who sprouts new limbs — and a midget who suddenly develops a huge sexual organ.

Tex, who wears a 10-gallon hat and directs most of his comments to a dog named Pinky, is astounded to learn about the shrine that”s grown up around Candy.

“My shiksa wife a virgin?” he proclaims. “The only miracle was if she could keep her legs closed for 20 minutes.”

Pursued by a state trooper (Kiefer Sutherland) who”s one of Candy”s many boyfriends, Tex steals Candy”s hand — a sequence reminiscent of “Sleeper,” where Allen”s character filches a nose — confesses to the priest and finally goes off to meet his fate.

“I”m afraid God is sending us all a message,” Tex says in conclusion. “If you can”t take a joke, go f- – – yourself.”

Some devout Catholics may not be laughing.

Catholic League president William Donohue is withholding judgment until he sees the movie, “but if they get into insulting the Virgin Mary, we”re not going to take it too kindly.”

But Andrew Goldman, director of programming planning for Cinemax, says executives at the cable service took the religious references “in the farcical vein in which it was intended. We”re very proud to show this movie.”

Goldman said he believes the producers, the Kushner-Locke Co. (which did not respond to inquiries), are still seeking a theatrical distributor for the film, which Cinemax picked up after a showing at the American Film Market in Los Angeles this spring.

“We deliberately scheduled it to coincidence with the release of (-ssq-)Small Time Crooks,”” Goldman said. “I understand that Woody loved the script [by first-timer Bill Wilson] and his participation attracted all the other stars to work for minimal salaries.”

Allen, who appears to have written or improvised many of his own lines, gives a daring, hilarious performance as Tex — his best in years.